Any benefit to putting up plastic over the insulation before hanging dry wall? Aside from time and minimal cost, any drawbacks?

The insulation does have a moisture barrier, but someone told be that covering it with plastic is a good idea, especially in a high moisture area, like a bathroom.
This wiil be in a closet that has one exterior wall and three interior, with one (the longest) separating the closet from a future bathroom.

Plastic is a bad vapor barrier..period. I would stick with the paper faced insulation and be done.
If you were to install plastic over the paper you would have 2 vapor barriers..can you see it raining in your home? This is a no-no in the vapor police book.

Paper lets the moisture collect a bit then releases it..plastic just runs down the wall. I have been in homes where the plywood at the exterior wall floor area was rotting through. These where extreme condition but better to er on the side of caution.